Exporting the Safari (OSX) window to a remote Linux box

I have network access to a headless Mac mini running "OS X Server" (10.6.8 Snow Leopard). Sitting on my Linux desktop (Fedora) I can execute something like:

ssh myuser@imachost xeyes

and get the xeyes window popping up in my desktop. Typical X behavior.

Now I want to bring a Safari window, but that fails. The most I can get is Safari getting launched locally on the OS X machine, but the window is not exported to my Linux. If a put a monitor to the Mac mini I see Safari window open there.

How can I accomplish this ? (I don't want to deal with VNC... don't want the full desktop - I just want it to behave like xeyes)...

(Linux geek here, but for OS X command line I'm kind of newbie...)